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Monday, December 25, 2017

We wish you all happy holidays! Whether or not you celebrate Christmas, we hope you have a peaceful time to relax and, if necessary, recover.

I want to use the opportunity to thank all of you for reading along, for giving me feedback, and for simply being interested in science in a time when that doesn’t seem to be normal anymore. A special “Thank you" to those who have sent donations. It is reassuring to know that you value this blog. It encourages me to keep my writing available here for free.

I’ll be tied up with family business during the coming week – besides the usual holiday festivities, the twins’ 7th birthday is coming up – so blogging will be sparse for some while.

Monday, December 18, 2017

The atomic nucleus consists of protons and neutrons. The protons and neutrons are themselves made of three quarks each, held together by gluons. That much is clear. But just how do the gluons hold the quarks together?

The quarks and gluons interact through the strong nuclear force. The strong nuclear force does not have only one charge – like electromagnetism – but three charges. The charges are called “colors” and often assigned the values red, blue, and green, but this is just a way to give names to mathematical properties. These colors have nothing to do with the colors that we can see.

Colors are a handy terminology because the charges blue, red, and green can combine to neutral (“white”) and so can a color and its anti-color (blue and anti-blue, green and anti-green, and so on). The strong nuclear force is mediated by gluons which each carry two types of colors. That the gluons themselves carry a charge means that, unlike the photon, they also interact among each other.

The strong nuclear force has the peculiar property that it gets stronger the larger the distance between two quarks, while it gets weaker on short distances. A handy metaphor for this is a rubber string – the more you stretch it, the stronger the restoring force. Indeed, this string-like behavior of the strong nuclear force is where string-theory originally came from.

The strings of the strong nuclear force are gluon flux-tubes, that are connections between two color-charged particles where the gluons preferably travel along. The energy of the flux-tubes is proportional to their length. If you have a particle (called a “meson”) made of a quark and an anti-quark, then the flux tube is focused on a straight line connecting the quarks. But what if you have three quarks, like inside a neutron or a proton?

According to the BBC, gluon flux-tubes (often depicted as springs, presumably because rubber is hard to illustrate) form a triangle.

At first sight it seems plausible that the gluons form a triangle because that requires the least stretching of strings that each connect two quarks. However, this triangular – “Δ-shaped” – configuration cannot connect three quarks and still maintain gauge-invariance. This means it violates the key principle of the strong force, which is bad and probably means this configuration is not physically possible. The Y-shaped flux-tubes on the other hand don’t suffer from that problem.

But we don’t have to guess around because this is physics and one can calculate it. This calculation cannot be done analytically but it is tractable by computer simulations. Bissey et al reported the results in a 2006 paper: “We do not find any evidence for the formation of a Delta-shaped flux-tube (empty triangle) distribution.” The conclusion is clear: The Y-shape is the preferred configuration.

And there’s more to learn! The quarks and gluons in the proton don’t sit still, and when they move then the center of the Y moves around. If you average over all possible positions you approximate a filled Δ-shape. (Though the temperature dependence is somewhat murky and subject of ongoing research.)

The flux-tubes also do not always exactly lie in the plane spanned by the three quarks but can move up and down into the perpendicular direction. So you get a filled Δ that’s inflated to the middle.

This distribution of flux tubes has nothing to do with the flavor of the quarks, meaning it’s the same for the proton and the neutron and all other particles composed of three quarks, such as the one containing two charm-quarks that was recently discovered at CERN. How did CERN picture the flux tubes? As a Δ:

Now you can claim you know quarks better than CERN! It’s either a Y or a filled triangle, but not an empty triangle.

I am not a fan of depicting gluons as springs because it makes me think of charged particles in a magnetic field. But I am willing to let this pass as creative freedom. I hope, however, that it is possible to get the flux-tubes right, and so I have summed up the situation in the image below :

Tuesday, December 12, 2017

Science has a problem. The present organization of academia discourages research that has tangible outcomes, and this wastes a lot of money. Of course scientific research is not exclusively pursued in academia, but much of basic research is. And if basic research doesn’t move forward, science by large risks getting stuck.

At the root of the problem is academia’s flawed reward structure. The essence of the scientific method is to test hypotheses by experiment and then keep, revise, or discard the hypotheses. However, using the scientific method is suboptimal for a scientist’s career if they are rewarded for research papers that are cited by as many of their peers as possible.

To the end of producing popular papers, the best tactic is to work on what already is popular, and to write papers that allow others to quickly produce further papers on the same topic. This means it is much preferable to work on hypotheses that are vague or difficult to falsify, and stick to topics that stay inside academia. The ideal situation is an eternal debate with no outcome other than piles of papers.

You see this problem in many areas of science. It’s origin of the reproducibility crisis in psychology and the life sciences. It’s the reason why bad scientific practices – like p-value hacking – prevail even though they are known to be bad: Because they are the tactics that keep researchers in the job.

It’s also why in the foundations of physics so many useless papers are written, thousands of guesses about what goes on in the early universe or at energies we can’t test, pointless speculations about an infinitude of fictional universes. It’s why theories that are mathematically “fruitful,” like string theory, thrive while approaches that dare introduce unfamiliar math starve to death (adding vectors to spinors, anyone?). And it is why physicists love “solving” the black hole information loss problem: because there’s no risk any of these “solutions” will ever get tested.

If you believe this is good scientific practice, you would have to find evidence that the possibility to write many papers about an idea is correlated with this idea’s potential to describe observation. Needless to say, there isn’t any such evidence.

What we witness here is a failure of science to self-correct.

It’s a serious problem.

I know it’s obvious. I am by no means the first to point out that academia is infected with perverse incentives. Books have beenwritten about it. Nature and Times Higher Education seem to publish a comment about this nonsense every other week. Sometimes this makes me hopeful that we’ll eventually be able to fix the problem. Because it’s in everybody’s face. And it’s eroding trust in science.

At this point I can’t even blame the public for mistrusting scientists. Because I mistrust them too.

Since it’s so obvious, you would think that funding bodies take measures to limit the waste of money. Yes, sometimes I hope that capitalism will come and rescue us! But then I go and read things like that Chinese scientists are paid bonuses for publishing in high impact journals. Seriously. And what are the consequences? As the MIT technology review relays:

“That has begun to have an impact on the behavior of some scientists. Wei and co report that plagiarism, academic dishonesty, ghost-written papers, and fake peer-review scandals are on the increase in China, as is the number of mistakes. “The number of paper corrections authored by Chinese scholars increased from 2 in 1996 to 1,234 in 2016, a historic high,” they say.”

If you think that’s some nonsense the Chinese are up to, look at what goes on in Hungary. They now have exclusive grants for top-cited scientists. According to a recent report in Nature:

“The programme is modelled on European Research Council grants, but with a twist: only those who have published a paper in the past five years that counted among the top 10% most-cited papers in their discipline are eligible to apply.”

What would you do to get such a grant?

To begin with, you would sure as hell not work on any topic that is not already pursued by a large number of your colleagues, because you need a large body of people able to cite your work to begin with.

You would also not bother criticize anything that happens in your chosen research area, because criticism would only serve to decrease the topic’s popularity, hence working against your own interests.

Instead, you would strive to produce a template for research work that can easily and quickly be reproduced with small modifications by everyone in the field.

What you get with such grants, then, is more of the same. Incremental research, generated with a minimum of effort, with results that meander around the just barely scientifically viable.

Clearly, Hungary and China introduce such measures to excel in national comparisons. They don’t only hope for international recognition, they also want to recruit top researchers hoping that, eventually, industry will follow. Because in the end what matters is the Gross Domestic Product.

Surely in some areas of research – those which are closely tied to technological applications – this works. Doing more of what successful people are doing isn’t generally a bad idea. But it’s not an efficient method to discover useful new knowledge.

That this is not a problem exclusive to basic research became clear to me when I read an article by Daniel Sarewitz in The New Atlantis. Sarewitz tells the story of Fran Visco, lawyer, breast cancer survivor, and founder of the National Breast Cancer Coalition:

“Ultimately, “all the money that was thrown at breast cancer created more problems than success,” Visco says. What seemed to drive many of the scientists was the desire to “get above the fold on the front page of the New York Times,” not to figure out how to end breast cancer. It seemed to her that creativity was being stifled as researchers displayed “a lemming effect,” chasing abundant research dollars as they rushed from one hot but ultimately fruitless topic to another. “We got tired of seeing so many people build their careers around one gene or one protein,” she says.”

So, no, lemmings chasing after fruitless topics are not a problem only in basic research. Also, the above mentioned overproduction of useless models is by no means specific to high energy physics:

“Scientists cite one another’s papers because any given research finding needs to be justified and interpreted in terms of other research being done in related areas — one of those “underlying protective mechanisms of science.” But what if much of the science getting cited is, itself, of poor quality?

Consider, for example, a 2012 report in Science showing that an Alzheimer’s drug called bexarotene would reduce beta-amyloid plaque in mouse brains. Efforts to reproduce that finding have since failed, as Science reported in February 2016. But in the meantime, the paper has been cited in about 500 other papers, many of which may have been cited multiple times in turn. In this way, poor-quality research metastasizes through the published scientific literature, and distinguishing knowledge that is reliable from knowledge that is unreliable or false or simply meaningless becomes impossible.”

Sarewitz concludes that academic science has become “an onanistic enterprise.” His solution? Don’t let scientists decide for themselves what research is interesting, but force them to solve problems defined by others:

“In the future, the most valuable science institutions […] will link research agendas to the quest for improved solutions — often technological ones — rather than to understanding for its own sake. The science they produce will be of higher quality, because it will have to be.”

As one of the academics who believe that understanding how nature works is valuable for its own sake, I think the cure that Sarewitz proposes is worse than the disease. But if Sarewitz makes one thing clear in his article, it’s that if we in academia don’t fix our problems soon, someone else will. And I don’t think we’ll like it.

Wednesday, December 06, 2017

Think fake news and echo chambers are a problem only in political discourse? Think again. You find many examples of myths and falsehoods on popular science pages. Most of them surround the hype of the day, but some of them have been repeated so often they now appear in papers, seminar slides, and textbooks. And many scientists, I have noticed with alarm, actually believe them.

Before I go and make my case, please ask yourself: If the cosmological constant was such a bad prediction, then what theory was ruled out by it? Nothing comes to mind? That’s because there never was such a prediction.

The myth has it that if you calculate the cosmological constant using the standard model of particle physics the result is 120 orders of magnitude larger than what is observed due to contributions from vacuum fluctuation. But this is wrong on at least 5 levels:

1. The standard model of particle physics doesn’t predict the cosmological constant, never did, and never will.

The cosmological constant is a free parameter in Einstein’s theory of general relativity. This means its value must be fixed by measurement. You can calculate a contribution to this constant from the standard model vacuum fluctuations. But you cannot measure this contribution by itself. So the result of the standard model calculation doesn’t matter because it doesn’t correspond to an observable. Regardless of what it is, there is always a value for the parameter in general relativity that will make the result fit with measurement.

Many theoretical physicists think the standard model is not a fundamental theory but must be amended at high energies. If that is so, then any calculation of the contribution to the cosmological constant using the standard model is wrong anyway. If there are further particles, so heavy that we haven’t yet seen them, these will play a role for the result. And we don’t know if there are such particles.

3. It’s idiotic to quote ratios of energy densities.

The 120 orders of magnitude refers to a ratio of energy densities. But not only is the cosmological constant usually not quoted as an energy density (but as a square thereof), in no other situation do particle physicists quote energy densities. We usually speak about energies, in which case the ratio goes down to 30 orders of magnitude.

4. The 120 orders of magnitude are wrong to begin with.

The actual result from the standard model scales with the fourth power of the masses of particles, times an energy-dependent logarithm. At least that’s the best calculation I know of. You find the result in equation (515) in this (awesomely thorough) paper. If you put in the numbers, out comes a value that scales with the masses of the heaviest known particles (not with the Planck mass, as you may have been told). That’s currently 13 orders of magnitude larger than the measured value, or 52 orders larger in energy density.

5. No one in their right mind ever quantifies the goodness of a prediction by taking ratios.

There’s a reason physicists usually talk a about uncertainty, statistical significance, and standard deviations. That’s because these are known to be useful to quantify the match of a theory with data. If you’d bother writing down the theoretical uncertainties of the calculation for the cosmological constant, the result would be compatible with the measured value even if you’d set the additional contribution from general relativity to zero.

In summary: No prediction, no problem.

Why does it matter? Because this wrong narrative has prompted physicists to aim at the wrong target.

The real problem with the cosmological constant is not the average value of the standard model contribution but – as Niayesh Afshordi elucidated better than I ever managed to – that the vacuum fluctuations, well, fluctuate. It’s these fluctuations that you should worry about. Because these you cannot get rid of by subtracting a constant.

But of course I know the actual reason you came here is that you want to know what is “the worst prediction in the history of physics” if not the cosmological constant...

I’m not much of a historian, so don’t take my word for it, but I’d guess it’s the prediction you get for the size of the universe if you assume the universe was born by a vacuum fluctuation out of equilibrium.

In this case, you can calculate the likelihood for observing a universe like our own. But the larger and the less noisy the observed universe, the less likely it is to originate from a fluctuation. Hence, the mere fact that you have a fairly ordered memory of the past and a sense of a reasonably functioning reality would be exceedingly tiny in such a case. So tiny, I’m not interested enough to even put in the numbers. (Maybe ask Sean Carroll.)

I certainly wish I’d never have to see the cosmological constant myth again. I’m not yet deluded enough to believe it will go away, but at least I now have this blogpost to refer to when I encounter it the next time.

Thursday, November 30, 2017

“Is this still science?” has become a recurring question in the foundations of physics. Whether it’s the multiverse, string theory, supersymmetry, or inflation, concerns abound that theoreticians have crossed a line.

On the one hand, I understand the concerns about breaking with centuries of tradition. We used to followed up each hypothesis with experimental test, and the longer the delay between hypothesis and test, the easier for pseudoscience to take foothold. On the other hand, I agree that speculation is a necessary part of science and new problems sometimes require new methods. Insisting on ideals of the past might mean getting stuck, maybe forever.

Even more important, I think it’s a grave mistake to let anyone define what we mean by doing science. Because who gets to decide what’s the right thing to do? Should we listen to Helge Kragh? Peter Woit? George Ellis? Or to the other side, to people like Max Tegmark, Sean Carroll, and David Gross, who claim we’re just witnessing a little paradigm change, nothing to worry about? Or should we, heaven forbid, listen to some philosophers and their ideas about post-empirical science?

There have been many previous attempts to define what science is, but the only definition that ever made sense to me is that science is what scientists do, and scientists are people who search for useful descriptions of nature. “Science,” then, is an emergent concept that arises in communities of people with a shared work practices. “Communities of practice,” as the sociologists say.

This brings me to my problem. If science is what scientists do, then how can anything that scientists do not be science? For a long time it seemed to me that in the end we won’t get around settling on a definition for science and holding on to it, regardless of how much I’d prefer a self-organized solution.

If some scientists insist on changing the old-fashioned methodology, the communities will fall apart. Let us call the two sectors “conservatives” and “progressives.” Each of them will insist they are the ones pursuing the more promising approach.

Based on this little theory, let me make a prediction what will happen next: The split will become more formally entrenched. Members of the community will begin taking sides, if they haven’t already, and will make an effort to state their research philosophy upfront.

In the end, only time will tell which lineage will survive and which one will share the fate of the Neanderthals.

So, if science is what scientists do, what happens if some scientists stop doing science? You see it happening as we speak.

From what I gather from Maeder’s list of publications, he’s an astrophysicist who recently had the idea to revolutionize cosmology by introducing a modification of general relativity. The paper which now makes headlines studies observational consequences of a model he introduced in January and claim to explain away the need for dark matter and dark energy. Both papers contain a lot of fits to data but no consistent theory. Since the man is known in the astrophysics community, however, the papers got published in ApJ, one of the best journals in the field.

For those of you who merely want to know whether you should pay attention to this new variant of modified gravity, the answer is no. The author does not have a consistent theory. The math is wrong.

For those of you who understand the math and want to know what the problem is, here we go.

Maeder introduces a conformal prefactor in front of the metric. You can always do that as an ansatz to solve the equations, so there is nothing modified about this, but also nothing wrong. He then looks at empty de Sitter space, which is conformally flat, and extracts the prefactor from there.

He then uses the same ansatz for the Friedmann Robertson Walker metric (eq 27, 28 in the first paper). Just looking at these equations you see immediately that they are underdetermined if the conformal factor (λ) is a degree of freedom. That’s because the conformal factor can usually be fixed by a gauge condition and be chosen to be constant. That of course would just give back standard cosmology and Maeder doesn’t want that. So he instead assumes that this factor has the same form as in de Sitter space.

Since he doesn’t have a dynamical equation for the extra field, my best guess is that this effectively amounts to choosing a weird time coordinate in standard cosmology. If you don’t want to interpret it as a gauge, then an equation is missing. Either way the claims which follow are wrong.
I can’t tell which is the case because the equations themselves just appear from nowhere. Neither of the papers contain a Lagrangian, so it remains unclear what is a degree of freedom and what isn’t. (The model is also of course not scale invariant, so somewhat of a misnomer.)

Maeder later also uses the same de Sitter prefactor for galactic solutions, which makes even less sense. You shouldn’t be surprised that he can fit some observations when you put in the scale of the cosmological constant to galactic models, because we have known this link since the 1980s. If there is something new to learn here, it didn’t become clear to me what.

Maeder’s papers have a remarkable number of observational fits and pretty plots, which I guess is why they got published. He clearly knows his stuff. He also clearly doesn’t know a lot about modifying general relativity. But I do, so let me tell you it’s hard. It’s really hard. There are a thousand ways to screw yourself over with it, and Maeder just discovered the one thousand and first one.

Wednesday, November 22, 2017

Mesosaurus fossil. Probably dating back to the early Permian Period, roughly 300 million years ago. [Image source]

Planet Earth formed around 4.5 billion years ago. The first primitive forms of life appeared about 4 billion years ago. Natural selection did the rest, giving rise to species increasingly better adapted to their environment. Evidence, as they say, is overwhelming.

Or is it? Imagine planet Earth began its existence a mere 10,000 years ago, with all fossil records in place and carbon-14 well into decaying. From there on, however, evolution proceeded as scientists tell us. How’d you prove this story wrong?

You can’t.

I know it hurts. But hang on there, band aid follows below.

You can’t prove this story wrong because of the way our current theories work. These theories need two ingredients: 1) A configuration at any one moment in time, called the “initial condition,” and 2) A hypothesis for how this initial configuration changes with time, called the “evolution law.”

You can reverse the evolution law to figure out from the present configuration what happened back in time. But there’s no way you can tell whether an earlier configuration actually existed or whether they are just convenient stories. In theories of this type – and that includes all theories in physics – you can therefore never rule out that at some earlier time the universe evolved by an entirely different law – maybe because God or The Programmer assembled it – and was then suddenly switched on to reproduce our observations.

I often hear people argue such creation-stories are wrong because they can’t be falsified, but this makes about as much sense as organic salt. No, they are not wrong, but they are useless.

Last week, I gave a talk at the department of History and Philosophy at the University of Toronto. My talk was followed by a “response” from a graduate student who evidently spent quite some time digging through this blog’s archives to classify my philosophy of science. I didn’t know I have one, but you never stop learning.

I learned that I am sometimes an anti-realist, meaning I don’t believe in the existence of an external reality. But I’d say I am neither a realist nor an anti-realist; I am agnostic about whether or not reality exists or what that even means. I don’t like to say science unveils “truths” about “reality” because this just brings on endless discussions about what is true and what is real. To me, science is about finding useful descriptions of the world, where by “useful” I mean they allow us to make predictions or explain already existing observations. The simpler an explanation, the more useful it is.

That scientific theories greatly simplify the stories we tell about the world is extremely important and embodies what we even mean by doing science. Forget all about Popperism and falsification, just ask what’s the most useful explanation. Saying that the world was created 10,000 years ago with all fossils in place is useless in terms of explaining the fossils. If you, on the other hand, extrapolate the evolution law back in time 4 billion years, you can start with a much simpler initial condition. That’s why it’s a better explanation. You get more out of less.

So there’s your band aid: Saying that the world was created 10,000 years ago with everything in place is unfalsifiable but also useless. It is quantifiably not simple: you need to put a lot of data into the initial condition. A much simpler, and thus scientifically better, explanation, is that planet Earth is ages old and Darwinian evolution did its task.

People often tell me that a finetuned initial condition doesn’t explain anything and thus isn’t scientific. Or, even weirder, that if you’d accept finetuned initial conditions this would turn science itself ad absurdum.

But this is just wrong. Finetuned initial conditions are equally good or bad explanations than not-finetuned ones. What is decisive isn’t whether the initial condition is finetuned, but whether it’s simple. According to current nomenclature, that is not the same thing. Absent a probability distribution, for example, an initial value of 1.0000000[00] for the curvature density parameter is scientifically equally good as an initial value of 0.0000001[00]… because both are equally simple. Current thinking among cosmologists, in contrast, has it that the latter is much worse than the former.

This confusion about what it means for a scientific theory to be useful sits deep and has caused a lot of cosmologists to cook up stories about the early universe based on highly questionable extrapolations into the past.

Take, for example, inflation, the idea that the early universe underwent a phase of rapid expansion. Inflation conjectures that before a certain moment in our universe’s history there was a different evolution law, assigned to a newly invented scalar field called the “inflaton.” But this conjecture is scientifically problematic because it construes up an evolution law in the past where we have no way of testing it. It’s not so different from saying that if you’d roll back time more than 10,000 years, you wouldn’t find planet Earth but god waving a magic wand or what have you.

A bold conjecture like inflation can only be justified if it leads to an actually simpler story, but on that the jury is out. Inflation was meant to solve several finetuning problems, but this doesn’t bring a simplification, it’s merely a beautification. The price to pay for this prettier theory, though, is that you now have at least one, if not several, new fields and their potentials, and some way to get rid of them again, which is arguably a complication of the story.

I wrote in a recent post that inflation seems justifiable after all because it provides a simple explanation for certain observed correlations in the cosmic microwave background (CMB). Well, that’s what I wrote some weeks ago, but now I am not so sure it is correct, thanks in no small part to a somewhat disturbing conversation I had with Niayesh Afshordi at Perimeter Institute.

The problem is that in cosmology there really aren’t a lot of data. There are but a few numbers. It’s a simple story already without inflation. And so, the current status is that I just don’t know whether or not inflation is a good theory. (But check back next month.)

Let me emphasize that the concordance model (aka ΛCDM) does not suffer from this problem. Indeed, it makes a good example for a scientifically successful theory. Here’s why.

For the concordance model, we seek the combination of dark matter, normal matter, and cosmological constant (as well as a handful other parameters) that best fit current observations. But what do we mean by best fit? We could use any combinations of parameters to get the dynamical law, and then use it to evolve the present day observations back in time. And regardless of what the law, there is always an initial state that will evolve into the present one.

In general, however, the initial state will be a mess, for example because the fluctuations of the cosmic microwave background (radiation) are not related in any obvious way to the structures we observe (matter). Whereas, if you pick the parameters correctly, these two types of structures belong together (higher density of matter corresponding to hotter spots in the cosmic microwave background). This match is a great simplification of the story – it explains something.

But the more you try to turn back time in the early universe, the harder it becomes to obey the scientific credo of storytelling, that you should seek only simpler explanations, not more complicated ones. The problem is the story we presently have is already very simple. This really is my biggest issue with eternal inflation and the multiverse or cyclic cosmologies, bounces, and so on and so forth. They are stories, all right, but they aren’t simplifying anything. They just add clutter, like the programmer that set up our universe so that it looks the way it looks.

On some days I hope something scientific will eventually come out of these stories. But today I am just afraid we have overstepped the limits of science.

Please be warned that things on this blog will go very slowly while I am away. On this occasion I want to remind you that I have comment moderation turned on. This means comments will not appear until I manually approve them. I usually check the queue at least once per day.

(The above image is the announcement for the New York event. Find the seven layout blunders.)

Friday, November 10, 2017

I was elated when I saw that Gian Francesco Giudice announced the “Dawn of the Post-Naturalness Era,” as the title of his recent paper promises. The craze in particle physics, I thought, might finally come to an end; data brought reason back to Earth after all.

But disillusionment followed swiftly when I read the paper.

Gian Francesco Giudice is a theoretical physicist at CERN. He is maybe not the most prominent member of his species, but he has been extremely influential in establishing “naturalness” as a criterion to select worthwhile theories of particle physics. Together with Riccardo Barbieri, Giudice wrote one of the pioneering papers on how to quantify naturalness, thereby significantly contributing to the belief that it is a scientific criterion. To date the paper has been cited more than 1000 times.

Giudice was also the first person I interviewed for my upcoming book about the relevance of arguments from beauty in particle physics. It became clear to me quickly, however, that he does not think naturalness is an argument from beauty. Instead, Giudice, like many in the field, believes the criterion is mathematically well-defined. When I saw his new paper, I hoped he’d come around to see the mistake. But I was overly optimistic.

As Giudice makes pretty clear in the paper, he still thinks that “naturalness is a well-defined concept.” I have previously explained why that is wrong, or rather why, if you make naturalness well-defined, it becomes meaningless. A quick walk through the argument goes as follows.

Naturalness in quantum field theories – ie, theories of the type of the standard model of particle physics – means that a theory at low energies does not sensitively depend on the choice of parameters at high energies. I often hear people say this means that “the high-energy physics decouples.” But note that changing the parameters of a theory is not a physical process. The parameters are whatever they are.

The processes that are physically possible at high energies decouple whenever effective field theories work, pretty much by definition of what it means to have an effective theory. But this is not the decoupling that naturalness relies on. To quantify naturalness you move around between theories in an abstract theory space. This is very similar to moving around in the landscape of the multiverse. Indeed, it is probably not a coincidence that both ideas became popular around the same time, in the mid 1990s.

If you now want to quantify how sensitively a theory at low energy depends on the choice of parameters at high energies, you first have to define the probability for making such choices. This means you need a probability distribution on theory space. Yes, it’s the exact same problem you also have for inflation and in the multiverse.

In most papers on naturalness, however, the probability distribution is left unspecified which implicitly means one chooses a uniform distribution over an interval of about length 1. The typical justification for this is that once you factor out all dimensionful parameters, you should only have numbers of order 1 left. It is with this assumption that naturalness becomes meaningless because you have now simply postulated that numbers of order 1 are better than other numbers.

You wanted to avoid arbitrary choices, but in the end you had to make an arbitrary choice. This turns the whole idea ad absurdum.

That you have to hand-select a probability distribution to make naturalness well-defined used to be well-known. One of the early papers on the topic clearly states

“The “theoretical license” at one’s discretion when making this choice [for the probability distribution] necessarily introduces an element of arbitrariness to the construction.”

Anderson and Castano, Phys. Lett. B 347:300-308 (1995)

Giudice too mentions “statistical comparisons” on theory space, so I am sure he is aware of the need to define the distribution. He also writes, however, that “naturalness is an inescapable consequence of the ingredients generally used to construct effective field theories.” But of course it is not. If it was, why make it an additional requirement?

(At this point usually someone starts quoting the decoupling theorem. In case you are that person let me say that a) no one has used mass-dependent regularization schemes since the 1980s for good reasons, and b) not only is it questionable to assume perturbative renormalizability, we actually know that gravity isn’t perturbatively renormalizable. In other words, it’s an irrelevant objection, so please let me go on.)

In his paper, Giudice further claims that “naturalness has been a good guiding principle” which is a strange thing to say about a principle that has led to merely one successful prediction but at least three failed predictions, more if you count other numerical coincidences that physicists obsess about like the WIMP miracle or gauge coupling unification. The tale of the “good guiding principle” is one of the peculiar myths that gets passed around in communities until everyone believes it.

Having said that, Giudice’s paper also contains some good points. He suggests, for example, that the use of symmetry principles in the foundations of physics might have outlasted its use. Symmetries might just be emergent at low energies. This is a fairly old idea which goes back at least to the 1980s, but it’s still considered outlandish by most particle physicists. (I discuss it in my book, too.)

Giudice furthermore points out that in case your high energy physics mixes with the low energy physics (commonly referred to as “UV/IR mixing”) it’s not clear what naturalness even means. Since this mixing is believed to be a common feature of non-commutative geometries and quite possibly quantum gravity in general, I have picked people’s brains on this for some years. But I only got shoulder shrugs, and I am none the wiser today. Giudice in his paper also doesn’t have much to say about the consequences other than that it is “a big source of confusion,” on which I totally agree.

But the conclusion that Giudice comes to at the end of his paper seems to be the exact opposite of mine.

I believe what is needed for progress in the foundations of physics is more mathematical rigor. Obsessing about ill-defined criteria like naturalness that don’t even make good working hypotheses isn’t helpful. And it would serve particle physicists well to identify their previous mistakes in order to avoid repeating them. I dearly hope they will not just replace one beauty-criterion by another.

Giudice on the other hand thinks that “we need pure unbridled speculation, driven by imagination and vision.” Which sounds great, except that theoretical particle physics has not exactly suffered from a dearth of speculation. Instead, it has suffered from a lack of sound logic.

Be that as it may, I found the paper insightful in many regards. I certainly agree that this is a time of crisis but that this is also an opportunity for change to the better. Giudice’s paper is very timely. It is also merely moderately technical, so I encourage you to give it a read yourself.

Monday, November 06, 2017

Popper is dead. Has been dead since 1994 to be precise. But also his philosophy, that a scientific idea needs to be falsifiable, is dead.

And luckily so, because it was utterly impractical. In practice, scientists can’t falsify theories. That’s because any theory can be amended in hindsight so that it fits new data. Don’t roll your eyes – updating your knowledge in response to new information is scientifically entirely sound procedure.

So, no, you can’t falsify theories. Never could. You could still fit planetary orbits with a quadrillion of epicycles or invent a luminiferous aether which just exactly mimics special relativity. Of course no one in their right mind does that. That’s because repeatedly fixed theories become hideously difficult, not to mention hideous, period. What happens instead of falsification is that scientists transition to simpler explanations.

To be fair, I think Popper in his later years backpedaled from his early theses. But many physicists not only still believe in Popper, they also opportunistically misinterpret the original Popper.

Even in his worst moments Popper never said a theory is scientific just because it’s falsifiable. That’s Popper upside-down and clearly nonsense. Unfortunately, upside-down Popper now drives theory-development, both in cosmology and in high energy physics.

It’s not hard to come up with theories that are falsifiable but not scientific. By scientific I mean the theory has a reasonable chance of accurately describing nature. (Strictly speaking it’s not an either/or criterion until one quantifies “reasonable chance” but it will suffice for the present purpose.)

I may predict for example, that Donald Trump will be shot by an elderly lady before his first term is over. That’s compatible with present knowledge and totally falsifiable. But chances it’s correct are basically zero and that makes it a prophecy, not a scientific theory.

The idea that falsifiability is sufficient to make a theory scientific is an argument I hear frequently from amateur physicists. “But you can test it!” they insist. Then they explain how their theory reworks the quantum or what have you. And post their insights in all-caps on my time-line. Indeed, as I am writing this, a comment comes in: “A good idea need only be testable,” says Uncle Al. Sorry, Uncle, but that’s rubbish.

You’d think that scientists know better. But two years ago I sat in a talk by Professor Lisa Randall who spoke about how dark matter killed the dinosaurs. Srsly. This was when I realized the very same mistake befalls professional particle physicists. Upside-down Popper is a widely-spread malaise.

Randall, you see, has a theory for particle dark matter with some interaction that allows the dark matter to clump within galaxies and form disks similar to normal matter. Our solar system, so the idea, periodically passes through the dark matter disk, which then causes extinction events. Or something like that.

Frankly I can’t recall the details, but they’re not so relevant. I’m just telling you this because someone asked “Why these dark matter particles? Why this interaction?” To which Randall’s answer was (I paraphrase) I don’t know but you can test it.

I don’t mean to pick on her specifically, it just so happens that this talk was the moment I understood what’s wrong with the argument. Falsifiability alone doesn’t make a theory scientific.

If the only argument that speaks for your idea is that it’s compatible with present data and makes a testable prediction, that’s not enough. My idea that Trump will get shot is totally compatible with all we presently know. And it does make a testable prediction. But it will not enter the annals of science, and why is that? Because you can effortlessly produce some million similar prophecies.

In the foundations of physics, compatibility with existing data is a high bar to jump, or so they want you to believe. That’s because if you cook up a new theory you first have to reproduce all achievements of the already established theories. This bar you will not jump unless you actually understand the present theories, which is why it’s safe to ignore the all-caps insights on my timeline.

But you can learn how to jump the bar. Granted, it will take you a decade. But after this you know all the contemporary techniques to mass-produce “theories” that are compatible with the established theories and make eternally amendable predictions for future experiments. In my upcoming book, I refer to these techniques as “the hidden rules of physics.”

These hidden rules tell you how to add particles to the standard model and then make it difficult to measure them, or add fields to general relativity and then explain why we can’t see them, and so on. Once you know how to do that, you’ll jump the bar every time. All you have to do then is twiddle the details so that your predictions are just about to become measureable in the next, say, 5 years. And if the predictions don’t work out, you’ll fiddle again.

And that’s what most theorists and phenomenologists in high energy physics live from today.

There are so many of these made-up theories now that the chances any one of them is correct are basically zero. There are infinitely many “hidden sectors” of particles and fields that you can invent and then couple so lightly that you can’t measure them or make them so heavy that you need a larger collider to produce them. The quality criteria are incredibly low, getting lower by the day. It’s a race to the bottom. And the bottom might be at asymptotically minus infinity.

This overproduction of worthless predictions is the theoreticians’ version of p-value hacking. To get away with it, you just never tell anyone how many models you tried that didn’t work as desired. You fumble things together until everything looks nice and then the community will approve. It’ll get published. You can give talks about it. That’s because you have met the current quality standard. You see this happen both in particle physics and in cosmology and, more recently, also in quantum gravity.

This nonsense has been going on for so long, no one sees anything wrong with it. And note how very similar this is to the dismal situation in psychology and the other life-sciences, where abusing statistics had become so common it was just normal practice. How long will it take for theoretical physicists to admit they have problems too?

Some of you may recall the book of philosopher Richard Dawid who claimed that the absence of alternatives speaks for string theory. This argument is wrong of course. To begin with there are alternatives to string theory, just that Richard conveniently doesn’t discuss them. But what’s more important is that there could be many alternatives that we do not know of. Richard bases his arguments on Bayesian reasoning and in this case the unknown number of unknown alternatives renders his no-alternative argument unusable.

But a variant of this argument illuminates what speaks against, rather than for, a theory. Let me call it the “Too Many Alternatives Argument.”

In this argument you don’t want to show that the probability for one particular theory is large, but that the probability for any particular theory is small. You can do this even though you still don’t know the total number of alternatives because you know there are at least as many alternatives as the ones that were published. This probabilistic estimate will tell you that the more alternatives have been found, the smaller the chances that any one of them is correct.

Really you don’t need Bayesian mysticism to see the logic, but it makes it sound more sciency. The point is that the easier it is to come up with predictions the lower their predictive value.

Duh, you say. I hear you. How come particle physicist think this is good scientific practice? It’s because of upside-down Popper! They make falsifiable predictions – and they believe that’s enough.

Yes, I know. I’m well on the way to make myself the most-hated person in high energy physics. It’s no fun. But look, even psychologists have addressed their problems by introducing better quality criteria. If they can do it, so can we.

Thursday, November 02, 2017

Max Tegmark just published his second book, “Life 3.0.” I gracefully declined reviewing it, seeing that three years weren’t sufficient to finish his first book. But thusly reminded of my shortfall, I made another attempt and finally got to the end. So here’s a late review or, if you haven’t made it through in three years either, a summary.

Tegmark is a cosmologist at MIT and his first book, “Our Mathematical Universe,” is about the idea that the world is not merely described by mathematics, but actually made of mathematics.

But. Well. People like Max don’t grow on trees. I have much sympathy for his free-range ideas and also, even though I’ve met him several times, I never really figured out what he was tenured for. Probably not the mathematical universe. Once upon a time, I was sure, he must have done actual physics.

Indeed, as the book reveals, Tegmark did CMB analysis before everyone else did it. This solid scientific ground is also where he begins his story: With engaging explanations of contemporary cosmology, the evolution of the universe, general relativity, and all that. He then moves on to inflation, eternal inflation and the multiverse, to quantum mechanics in general and the many worlds interpretation in particular. After this, he comes to the book’s main theme, the mathematical universe hypothesis. At that point we’re at page 250 or so.

Tegmark writes well. He uses helpful analogies and sprinkles some personal anecdotes which makes the topic more digestible. The book also has a lot of figures, about half of which are helpful. I believe I have seen most of them on his slides.

Throughout the book, Tegmark is careful to point out where he leaves behind established science and crosses over into speculation. However, by extrapolating from the biased sample of people-he-spends-time-with, Tegmark seems to have come to believe the multiverse is much more accepted than is the case. Still, it is certainly a topic that is much discussed and worth writing about.

But even though Tegmark’s story flows nicely, I got stuck over and over again. The problem isn’t that the book is badly written. The problem is that, to paraphrase John Mellencamp, the book goes on long after the thrill of reading is gone.

Already in the first parts of the book, Tegmark displays an unfortunate tendency to clutter his arguments with dispensable asides. I got the impression he is so excited about writing that, while at it, he just also has to mention this other thing that he once worked on, and that great idea he had which didn’t work, and why that didn’t work, and how that connects with yet something else. And did I mention that? By the way, let me add this. Which is related to that. And a good friend of mine thinks so. But I don’t think so. And so on.

And then, just when you think the worst is over, Tegmark goes on to tell you what he thinks about alien life and consciousness and asteroid impacts and nuclear war and artificial intelligence.

To me, his writing exhibits a familiar dilemma. If you’ve spent years thinking about a topic, the major challenge isn’t deciding what to tell the reader. It’s deciding what to not tell them. And while some readers may welcome Tegmark’s excursions, I suspect that many of them will have trouble seeing the connections that he, without any doubt, sees so clearly.

As to the content. The major problems with Max’s idea that the universe is made of mathematics rather than merely described by mathematics are:

The hypothesis is ill-defined without explaining what “is real” means. I therefore don’t know what’s the point even talking about it.

Leaving this aside, Max erroneously thinks it’s the simplest explanation for why mathematics is so useful, and hence supported by Ockham’s razor (though he doesn’t explicitly say so).
The argument is that if reality is merely described by mathematics rather than actually made of mathematics, then one needs an additional criterion to define what makes some things real and others not.

But that argument is logically wrong. Saying that the universe is accurately described by mathematics makes no assumption about whether it “really is” mathematics (scare quotes to remind you that that’s ill-defined). It is unnecessary to specify whether the universe is mathematics or is something more, evidenced by scientists never bothering with such a specification. Ockham’s razor thus speaks against the mathematical universe.

He claims that a theory which is devoid of “human baggage” must be formulated in mathematics. I challenge you to prove this, preferably without using human baggage. If that was too meta: Just because we don’t know anything better than math to describe nature doesn’t mean there is nothing.

Max also erroneously thinks, or at least claims in the book, that the mathematical universe hypothesis is testable. Because, so he writes, it predicts that we will continue to find mathematical descriptions for natural phenomena.

But of course if there was something for which we do not manage to find a mathematical description, that would never prove the mathematical universe wrong. After all, it might merely mean we were too dumb to figure out the math. Now that I think of it, maybe our failure to quantize gravity falsifies the mathematical universe.

There are further various statements in the book which I can’t make sense of. For example, I have no idea what an “element” of a mathematical structure is. I only know elements of sets. I also don’t understand why Tegmark believes accepting that our universe is a mathematical structure means that differential equations no longer need initial conditions. Or so he seems to say. Even more perplexing, he argues that the multiverse explains why the constants of nature seem finetuned for the existence of life. This is a misunderstanding of both finetuning and the anthropic principle.

There. I’ve done it again. I set out with the best intention to say nice things, but all that comes out is “wrong, wrong, wrong.”

To work off my guilt, I’ll now have to buy his new book too. Check back in three years.

It is correct that noncommutative geometry plays a role in many approaches to quantum gravity and it’s not an entirely uninteresting idea. However, the variant that the authors want to test in the paper is not of the commonly discussed type. They want the effect to be relevant for the center-of-mass coordinates, so that it scales with the total mass. That assumption has no support from any approach to quantum gravity. It’s made-up. It is also mathematically highly problematic.

Third, I already spelled out in my review several years ago that this is bogus (see section 4.6) and doesn’t follow from anything. Though the academically correct phrase I used there is “should be regarded with caution.”

Fourth, note that the paper appeared on the arxiv two weeks after being accepted for publication. The authors clearly were not keen on any comment by any blogger before they had made it through peer review.

The publishing business continues to surprise me. I have no idea who wrote the text accompanying the Amazon page and, for all I can tell, the first sentence doesn’t even make sense grammatically. Neither, for that matter, did I have anything to do with the cover image. But well, it’s dark, which is fitting enough.

The book is about the role of arguments from beauty, naturalness, and elegance in the foundations of physics, by which I mean high energy physics, cosmology, quantum gravity, and quantum foundations. Or at least that’s what I thought the book would be about. What the book really is about is how to abuse mathematics while pretending to do science.

The structure I chose is somewhat unusual for a popular science book. It’s a series of interviews I conducted, interlaced with explanations of the subject matter, and a broader narrative for context. Among the people I interviewed are Nima Arkani-Hamed, Frank Wilczek, Steven Weinberg, Garrett Lisi, and George Ellis.

You see, I did everything I could to make sure you really, really had to buy the book.

I also interviewed Gian Francesco Giudice, who is maybe not as well-known as the above-named, but who has been a key figure in the naturalness-movement in high-energy physics. Interestingly, he just yesterday posted a paper on the arXiv on what is also a central theme in the book.

To complete the list of interviewees: I also spoke to Michael Krämer, a SUSY phenomenologist in Aachen who unwittingly set me off on this whole enterprise, Keith Olive (also a high-energy phenomenologist), Joe Polchinski (a string theorist), Gordon Kane (the only person on the planet able to derive predictions from string theory), Katherine Mack (an astrophysicist), Chad Orzel (he who teaches physics to dogs), Xiao Gang-Wen (a condensed matter physicist with a theory of everything) and Doyne Farmer (a physicist turned economist).

I also interviewed Howard Baer and Gerard 't Hooft, but the two didn’t make the final cut and only appear in a short sentence each. I swear, throwing them out was the hardest part of writing the whole book.

While the book focuses on physics, my aim is much more general. The current situation in the foundations of physics is a vivid example for how science fails to self-correct. The reasons for this failure, as I lay out in the book, are unaddressed social and cognitive biases. But this isn't a problem specific to the foundations of physics. It’s a problem that befalls all disciplines, just that in my area the prevalence of not-so-scientific thinking is particularly obvious due to the lack of data.

This isn’t a nice book and sadly it’s foreseeable most of my colleagues will hate it. By writing it, I waived my hopes of ever getting tenure. This didn’t come easily to me. But I have waited two decades for things to change and they didn’t change and I came to conclude at the very least I can point at the problems I see.

If you care about progress in the foundations of physics, please preorder the book. Also follow me on facebook or twitter for further updates. You don’t have to wait for the book’s content to appear on this blog, it won’t happen.

Sunday, October 22, 2017

The recently reported gravitational wave detection, GW170817, was accompanied by electromagnetic radiation. Both signals arrived on Earth almost simultaneously, within a time-window of a few seconds. This is a big problem for some alternatives to dark matter as this new paper lays out:

The observation is difficult to explain with some variants of modified gravity because in these models electromagnetic and gravitational radiation travel differently.

In modified gravity, dark matter is not made of particles. Instead, the gravitational pull felt by normal matter comes from a gravitational potential that is not the one predicted by general relativity. In general relativity and its modifications likewise, the gravitational potential is described by the curvature of space-time and encoded in what is called the “metric.” In the versions of modified gravity studied in the new paper, the metric has additional terms which effectively act on normal matter as if there was dark matter, even though there is no dark matter.

However, the metric in general relativity is also what gives rise to gravitational waves, which are small, periodic disturbances of that metric. If dark matter is made of particles, then the gravitational waves themselves travel through the gravitational potential of normal plus dark matter. If dark matter, however, is due to a modification of the gravitational potential, then gravitational waves themselves do not feel the dark matter potential.

This can be probed if you send both types of signals, electromagnetic and gravitational, through a gravitational potential, for example that of the Milky Way. The presence of the gravitational potential increases the run-time of the signal, and the deeper the potential, the longer the run-time. This is known as “Shapiro-delay” and is one of the ways, for example, to probe general relativity in the solar system.

The authors of the paper put in the numbers and find that the difference between the potential with dark matter for electromagnetic radiation and the potential without dark matter for gravitational radiation adds up to about a year for the Milky Way alone. On top come some hundred days more delay if you also take into account galaxies that the signals passed by on the way from the source to Earth. If correct, this means that the almost simultaneous arrival of both signals rules out the modifications of gravity which lead to differences in the travel-time by many orders of magnitude.

The logic of the argument is this. We know that galaxies cause gravitational lensing as if they contain dark matter. This means even if dark matter can be ascribed to modified gravity, its effect on light must be like that of dark matter. The Shapiro-delay isn’t exactly the same as gravitational lensing, but the origin of both effects is mathematically similar. This makes it plausible that the Shapiro-delay for electromagnetic radiation scales with the dark matter mass, regardless of its origin. The authors assume that the delay for the gravitational waves in modified gravity is just due to normal matter. This means that gravitational waves should arrive much sooner than their electromagnetic company because the potential the gravitational waves feel is much shallower.

The Shapiro-delay on the Sun is about 10-4 seconds. If you scale this up to the Milky Way, with a mass of about 1012 times that of the Sun, this gives 108 seconds, which is indeed about a year or so. You gain a little since the dark matter mass is somewhat higher and lose a little because the Milky Way isn’t spherically symmetric. But by order of magnitude this simple estimate explains the constraint.

The paper hence rules out all modified gravity theories that predict gravitational waves which pass differently through the gravitational potential of galaxies than electromagenetic waves do. This does not affect all types of modified gravity, but it does affect, according to the paper, Bekenstein’s TeVeS and Moffat’s Scalar-Vector-Tensor theory.

A word of caution, however, is that the paper does not contain, and I have not seen, an actual calculation for the delay of gravitational waves in the respective modified gravity models. Though the estimate seems good, it’s sketchy on the math.

I think the paper is a big step forward. I am not sold on either modified gravity or particle dark matter and think both have their pros and cons. To me, particle dark matter seems plausible and it works well on all scales, while modified gravity doesn’t work so well on cosmological (super-galactic) scales. On the other hand, we haven’t directly measured any dark matter particles, and some of the observed regularities in galaxies are not well explained by the particle-hypothesis.

But as wonderful as it is to cross some models off the list, ruling out certain types of modified gravity doesn’t make particle dark matter any better. The reason you never hear anyone claim that particle dark matter has been ruled out is that it’s not possible to rule it out. The idea is so flexible and the galactic simulations have so many parameters you can explain everything.

This is why I have lately been intrigued by the idea that dark matter is a kind of superfluid which, in certain approximations, behaves like modified gravity. This can explain the observed regularities while maintaining the benefits of particle dark matter. For all I can tell, the new constraint doesn’t apply to this type of superfluid (one of the authors of the new paper confirmed this to me).

In summary, let me emphasize that this new observation doesn’t rule out modified gravity any more than the no-detection of Weakly Interacting Massive Particles rules out particle dark matter. So please don’t jump to conclusions. It rules out certain types of modified gravity, no more and no less. But this paper gives me hope that a resolution of the dark matter mystery might happen in my lifetime.

Friday, October 20, 2017

Physicists have gathered evidence that space-time can behave like a fluid. Mathematical evidence, that is, but still evidence. If this relation isn’t a coincidence, then space-time – like a fluid – may have substructure.

We shouldn’t speak of space and time as if the two were distant cousins. We have known at least since Einstein that space and time are inseparable, two hemispheres of the same cosmic brain, joined to a single entity: space-time. Einstein also taught us that space-time isn’t flat, like a paper, but bent and wiggly, like a rubber sheet. Space-time curves around mass and energy, and this gives rise to the effect we call gravity.

That’s what Einstein said. But turns out if you write down the equations for small wiggles in a medium – such as soundwaves in a fluid – then the equations look exactly like those of waves in a curved background.

Yes, that’s right. Sometimes, waves in fluids behave like waves in a curved space-time; they behave like waves in a gravitational field. Fluids, therefore, can be used to simulate gravity. And that’s some awesome news because this correspondence between fluids and gravity allows physicists to study situations that are otherwise experimentally inaccessible, for example what happens near a black hole horizon, or during the rapid expansion in the early universe.

This mathematical relation between fluids and gravity is known as “analog gravity.” That’s “analog” as in “analogy” not as opposed to digital. But it’s not just math. The first gravitational analogies have meanwhile been created in a laboratory.

Most amazing is the work by Jeff Steinhauer at Technion, Israel. Steinhauer used a condensate of supercooled atoms that “flows” in a potential of laser beams which simulate the black hole horizon. In his experiment, Steinhauer wanted to test whether black holes emit radiation as Stephen Hawking predicted. The temperature of real, astrophysical, black holes is too small to be measurable. But if Hawking’s calculation is right, then the fluid-analogy of black holes should radiate too.

Black holes trap light behind the “event horizon.” A fluid that simulates a black hole doesn’t trap light, it traps instead the fluid’s soundwaves behind what is called the “acoustic horizon.” Since the fluid analogies of black holes aren’t actually black, Bill Unruh suggested to call them “dumb holes.” The name stuck.

But whether the horizon catches light or sound, Hawking-radiation should be produced regardless, and it should appear in form of fluctuations (in the fluid or quantum matter fields, respectively) that are paired across the horizon.

Steinhauer claims he has measured Hawking-radiation produced by an acoustic black hole. His results are presently somewhat controversial – not everyone is convinced he has really measured what he claims he did – but I am sure sooner or later this will be settled. More interesting is that Steinhauer’s experiment showcases the potential of the method.

Of course fluid-analogies are still different from real gravity. Mathematically the most important difference is that the curved space-time which the fluid mimics has to be designed. It is not, as for real gravity, an automatic reaction to energy and matter; instead, it is part of the experimental setup. However, this is a problem which at least in principle can be overcome with a suitable feedback loop.

The conceptually more revealing difference is that the fluid’s correspondence to a curved space-time breaks down once the experiment starts to resolve the fluid’s atomic structure. Fluids, we know, are made of smaller things. Curved space-time, for all we presently know, isn’t. But how certain are we of this? What if the fluid analogy is more than an analogy? Maybe space-time really behaves like a fluid; maybe it is a fluid. And if so, the experiments with fluid-analogies may reveal how we can find evidence for a substructure of space-time.

Some have pushed the gravity-fluid analogy even further. Gia Dvali from LMU Munich, for example, has proposed that real black holes are condensates of gravitons, the hypothetical quanta of the gravitational field. This simple idea, he claims, explains several features of black holes which have so-far puzzled physicists, notably the question how black holes manage to keep the information that falls into them.

We used to think black holes are almost featureless round spheres. But if they are instead, as Dvali says, condensates of many gravitons, then black holes can take on many slightly different configuration in which information can be stored. Even more interesting, Dvali proposes the analogy could be used to design fluids which are as efficient at storing and distributing information as black holes are. The link between condensed matter and astrophysics, hence, works both ways.

Physicists have looked for evidence of space-time being a medium for some while. For example by studying light from distant sources, such as gamma-ray bursts, they tried to find out whether space has viscosity or whether it causes dispersion (a running apart of frequencies like in a prism). A new line of research is to search for impurities – “space-time defects” – like crystals have them. So far the results have been negative. But the experiments with fluid analogies might point the way forward.

If space-time is made of smaller things, this could solve a major problem: How to describe the quantum behavior of space time. Unlike all the other interactions we know of, gravity is a non-quantum theory. This means it doesn’t fit together with the quantum theories that physicists use for elementary particles. All attempts to quantize gravity so-far have either failed or remained unconfirmed speculations. That space itself isn’t fundamental but made of other things is one way to approach the problem.

Not everyone likes the idea. What irks physicists most about giving substance to space-time is that this breaks Einstein’s bond between space and time which has worked dramatically well – so far. Only further experiment will reveal whether Einstein’s theory holds up.

Tuesday, October 17, 2017

I’ve had many interesting reactions to my recent post about inflation, this idea that the early universe expanded exponentially and thereby flattened and smoothed itself. The maybe most interesting response to my pointing out that inflation doesn’t solve the problems it was invented to solve is a flabbergasted: “But everyone else says it does.”

Not like I don’t know that. But, yes, most people who work on inflation don’t even get the basics right.

I’m not sure why that is so. Those who I personally speak with pretty quickly agree that what I say is correct. The math isn’t all that difficult and the situation pretty clar. The puzzle is, why then do so many of them tell a story that is nonsense? And why do they keep teaching it to students, print it in textbooks, and repeat it in popular science books?

I am fascinated by this for the same reason I’m fascinated by the widely-spread and yet utterly wrong idea that the Bullet-cluster rules out modified gravity. As I explained in an earlier blogpost, it doesn’t. Never did. The Bullet-cluster can be explained just fine with modified gravity. It’s difficult to explain with particle dark matter. But, eh, just the other day I met a postdoc who told me the Bullet-cluster rules out modified gravity. Did he ever look at the literature? No.

One reason these stories survive – despite my best efforts to the contrary – is certainly that they are simple and sound superficially plausible. But it doesn’t take much to tear them down. And that it’s so simple to pull away the carpet under what motivates research of thousands of people makes me very distrustful of my colleagues.

Let us return to the claim that inflation solves the flatness problem. Concretely, the problem is that in cosmology there’s a dynamical variable (ie, one that depends on time), called the curvature density parameter. It’s by construction dimensionless (doesn’t have units) and its value today is smaller than 0.1 or so. The exact digits don’t matter all that much.

What’s important is that this variable increases in value over time, meaning it must have been smaller in the past. Indeed, if you roll it back to the Planck epoch or so, it must have been something like 10-60, take or give some orders of magnitude. That’s what they call the flatness problem.

Now you may wonder, what’s problematic about this. How is it surprising that the value of something which increases in time was smaller in the past? It’s an initial value that’s constrained by observation and that’s really all there is to say about it.

It’s here where things get interesting: The reason that cosmologists believe it’s a problem is that they think a likely value for the curvature density at early times should have been close to 1. Not exactly one, but not much smaller and not much larger. Why? I have no idea.

Each time I explain this obsession with numbers close to 1 to someone who is not a physicist, they stare at me like I just showed off my tin foil hat. But, yeah, that’s what they preach down here. Numbers close to 1 are good. Small or large numbers are bad. Therefore, cosmologists and high-energy physicists believe that numbers close to 1 are more likely initial conditions. It’s like a bizarre cult that you’re not allowed to question.

But if you take away one thing from this blogpost it’s that whenever someone talks about likelihood or probability you should ask “What’s the probability distribution and where does it come from?”

The probability distribution is what you need to define just how likely each possible outcome is. For a fair dice, for example, it’s 1/6 for each outcome. For a not-so-fair dice it could be any combination of numbers, so long as the probabilities all add to 1. There are infinitely many probability distributions and without defining one it is not clear what “likely” means.

If you ask physicists, you will quickly notice that neither for inflation nor for theories beyond the standard model does anyone have a probability distribution or ever even mentions a probability distribution for the supposedly likely values.

How does it matter?

The theories that we currently have work with differential equations and inflation is no exception. But the systems that we observe are not described by the differential equations themselves, they are described by solutions to the equation. To select the right solution, we need an initial condition (or several, depending on the type of equation). You know the drill from Newton’s law: You have an equation, but you only can tell where the arrow will fly if you also know the arrow’s starting position and velocity.

The initial conditions are either designed by the experimenter or inferred from observation. Either way, they’re not predictions. They can not be predicted. That would be a logical absurdity. You can’t use a differential equation to predict its own initial conditions. If you want to speak about the probability of initial conditions you need another theory.

What happens if you ignore this and go with the belief that the likely initial value for the curvature density should be about 1? Well, then you do have a problem indeed, because that’s incompatible with data to a high level of significance.

Inflation then “solves” this supposed problem by taking the initial value and shrinking it by, I dunno, 100 or so orders of magnitude. This has the consequence that if you start with something of order 1 and add inflation, the result today is compatible with observation. But of course if you start with some very large value, say 1060, then the result will still be incompatible with data. That is, you really need the assumption that the initial values are likely to be of order 1. Or, to put it differently, you are not allowed to ask why the initial value was not larger than some other number.

This fineprint, that there are still initial values incompatible with data, often gets lost. A typical example is what Jim Baggot writes in his book “Origins” about inflation:

“when inflation was done, flat spacetime was the only result.”

Well, that’s wrong. I checked with Jim and he totally knows the math. It’s not like he doesn’t understand it. He just oversimplifies it maybe a little too much.

But it’s unfair to pick on Jim because this oversimplification is so common. Ethan Siegel, for example, is another offender. He writes:

“if the Universe had any intrinsic curvature to it, it was stretched by inflation to be indistinguishable from “flat” today.”

That’s wrong too. It is not the case for “any” intrinsic curvature that the outcome will be almost flat. It’s correct only for initial values smaller than something. He too, after some back and forth, agreed with me. Will he change his narrative? We will see.

You might say then, but doesn’t inflation at least greatly improve the situation? Isn’t it better because it explains there are more values compatible with observation? No. Because you have to pay a price for this “explanation:” You have to introduce a new field and a potential for that field and then a way to get rid of this field once it’s done its duty.

I am pretty sure if you’d make a Bayesian estimate to quantify the complexity of these assumptions, then inflation would turn out to be more complicated than just picking some initial parameter. Is there really any simpler assumption than just some number?

Some people have accused me of not understanding that science is about explaining things. But I do not say we should not try to find better explanations. I say that inflation is not a better explanation for the present almost-flatness of the universe than just saying the initial value was small.

Shrinking the value of some number by pulling exponential factors out of thin air is not a particularly impressive gimmick. And if you invent exponential factors already, why not put them into the probability distribution instead?

Let me give you an example for why the distinction matters. Suppose you just hatched from an egg and don’t know anything about astrophysics. You brush off a loose feather and look at our solar system for the first time. You notice immediately that the planetary orbits almost lie in the same plane.

Now, if you assume a uniform probability distribution for the initial values of the orbits, that’s an incredibly unlikely thing to happen. You would think, well, that needs explaining. Wouldn’t you?

The inflationary approach to solving this problem would be to say the orbits started with random values but then some so-far unobserved field pulled them all into the same plane. Then the field decayed so we can’t measure it. “Problem solved!” you yell and wait for the Nobel Prize.

But the right explanation is that due to the way the solar system formed, the initial values are likely to lie in a plane to begin with! You got the initial probability distribution wrong. There’s no fancy new field.

In the case of the solar system you could learn to distinguish dynamics from initial conditions by observing more solar systems. You’d find that aligned orbits are the rule not the exception. You’d then conclude that you should look for a mechanism that explains the initial probability distribution and not a dynamical mechanism to change the uniform distribution later.

In the case of inflation, unfortunately, we can’t do such an observation since this would require measuring the initial value of the curvature density in other universes.

While I am at it, it’s interesting to note that the erroneous argument against the heliocentric solar system, that the stars would have to be “unnaturally” far away, was based on the same mistake that the just-hatched chick made. Astronomers back then implicitly assumed a probability distribution for distances between stellar objects that was just wrong. (And, yes, I know they also wrongly estimated the size of the stars.)

In the hope that you’re still with me, let me emphasize that nevertheless I think inflation is a good theory. Even though it does not solve the flatness problem (or monopole problem or horizon problem) it explains certain correlations in the cosmic-microwave-background. (ET anticorrelations for certain scales, shown in the figure below.)

In the case of these correlations, adding inflation greatly simplifies the initial condition that gives rise to the observation. I am not aware that someone actually has quantified this simplification but I’m sure it could be done (and it should be done). Therefore, inflation actually is the better explanation. For the curvature, however, that isn’t so because replacing one number with another number times some exponential factor doesn’t explain anything.

I hope that suffices to convince you that it’s not me who is nuts.

I have a lot of sympathy for the need to sometimes oversimplify scientific explanations to make them accessible to non-experts. I really do. But the narrative that inflation solves the flatness problem can be found even in papers and textbooks. In fact, you can find it in the above-mentioned lecture notes! It’s about time this myth vanishes from the academic literature.